# Jacob Eliosoff's EMA (exponential moving average) difficulty algorithm
# https://en.wikipedia.org/wiki/Moving_average#Application_to_measuring_computer_performance
# see https://github.com/zawy12/difficulty-algorithms/issues/1 for other algos
# ST = solvetime, T=target solvetime
# height = most recently solved block
# There's a "2" in the exponent below to make the above N comparable to SMA, WT-144, & WWHM
# MTP should not be used

T=<target solvetime>
# Ideal N appears to be N= 40 to 85 for T=600 to 60 by the following formula.
# see https://github.com/zawy12/difficulty-algorithms/issues/14

N=int(50*(600/T)^0.3)

# Choose a limit on on how large solvetimes can be based on keeping
# difficulty from dropping more than 20% per bad timestamp.
# Varies from 5 for N < 50 to 9 for N > 76.
# The way it is used in the code makes it a symmetrical limit.
limit = max(5,min(int(N/0.90)-N,9))

maxT=timestamp[height-limit-1]
for ( i = height - limit to i < height )  { maxT = max(maxT, timestamp[i]) }
ST = timestamp[height] - maxT 
ST = max(T/200,min(T*limit, ST))
next_D = previous_D * ( T/ST + e^(-ST*2/T/N) * (1-T/ST) )